Multi-dimensional hybrid and transpose form finite impulse response filters

ABSTRACT

Multi-dimensional finite impulse response filters ale disclosed in hybrid and transpose forms. Multi-dimensional signals can be expressed in a vector (ox matrix) form to allow multi-dimensional signals to be processed collectively. Known hybrid and transpose FIR filters are extended to the multi-dimensional case to allow multi-dimensional signals to be processed with reduced redundancies. The input signals are vectors with multidimensional components. The disclosed FIR filters include multipliers that perform matrix multiplications with multiple coefficients, and adders for performing vector additions with multiple inputs and outputs. The z-transforms are provided for the disclosed hybrid and transpose multi-dimensional FIR filters.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/610,336, filed Jun. 30, 2003 now U.S. Pat. No. 7,263,541, whichclaims the benefit of U.S. Provisional Application No. 60/443,258, filedJan. 28, 2003; and is related to U.S. patent application Ser. No.10/610,335 entitled, “Method and Apparatus for Reducing Noise In anUnbalanced Channel Using Common Mode Component,” and U.S. patentapplication Ser. No. 10/610,334 entitled, “Method And Apparatus ForReducing Cross-Talk With Reduced Redundancies,” each incorporated byreference herein.

FIELD OF THE INVENTION

The present invention relates generally to digital filter designs, andmore particularly, to multi-dimensional finite impulse response filters.

BACKGROUND OF THE INVENTION

Digital filters are commonly employed in signal processing applications.U.S. Pat. No. 5,983,254 to Azadet discloses a number of known finiteimpulse response (FIR) filter implementations. For example, FIG. 1 showsan FIR filter in the hybrid form. The hybrid form has a reduced numberof delay elements overall (relative to the direct and transpose forms),with delay elements in both the input and output paths. The exemplaryconventional hybrid FIR filter 100 shown in FIG. 1 has three modules110-1 through 110-3. Each module, such as module 110-1, provides threetaps at multipliers 115-1, 115-2 and 115-3, respectively. Each module110 includes the same number of delay elements as the number of taps.The delay elements may be embodied, for example, as shift registers.Specifically, delay elements 105-1 and 105-2 are disposed on input path101, and delay element 105-3 is disposed on output path 111. Delayelement 105-2 is inserted between multipliers 115-1 and 115-2. Delayelement 105-2 is inserted between multipliers 115-2 and 115-3. Adder120-3 receives a delayed sum generated by adder 120-4 and a productgenerated by multiplier 115-3 and generates a sum. Adder 120-2 receivesthe sum generated by adder 120-3 and a product generated by multiplier115-2 and generates a sum. Adder 120-1, disposed on output path 111,receives the sum generated by adder 120-2 and a product generated bymultiplier 115-1 and generates a sum.

The filter weights for the modules 110-1 through 110-3 shown in FIG. 1are scalar values, w₀ through w₈. With the above filter arrangement, thez-transform of the transfer function of filter 100, H(z), can beexpressed as follows:H(z)=z ⁻¹ {w ₀ +w ₁ z ⁻¹ +w ₂ z ⁻² }+z ⁻³ {w ₃ +w ₄ z ⁻¹ +w ₅ z⁻²}+  (1)where the first term z⁻¹{w₀+w₁z⁻¹+w₂z⁻²} corresponds to module 110-1;and the second term z⁻³{w₃+w₄z⁻¹+w₅z⁻²} corresponds to module 110-2. Itcan be shown that the hybrid form FIR filter 100 shown in FIG. 1 isfunctionally equivalent to a direct form FIR filter and a transpose formFIR filter (although, beneficially, with fewer delay elements). For amore detailed discussion of such FIR filters, see, for example, U.S.Pat. No. 5,983,254, incorporated by reference herein.

A number of applications require multi-dimensional signals to beprocessed on FIR filters, such as the FIR filter 100 shown in FIG. 1.For example, two-dimensional and three-dimensional signals are oftenprocessed using FIR filters in image filtering and video processingapplications. Each dimension of the multi-dimensional signal, however,is typically processed independently. Frequently, however, redundanciesresult from the same operation, such as a delay, being applied to thesame input signal multiple times as each dimension is independentlyprocessed. For example, conventional cross-talk cancellers typicallyconsider the same signal on a given twisted pair multiple times in orderto reduce the echo on the same twisted pail, as well as the near endcross-talk on each of the other twisted pairs. In the case of fourtwisted pairs, for example, there is a factor-of-four redundancy, sincea given signal is used once for the echo cancellation on the sametwisted pair and three additional times for the near end cross-talk onthe other three twisted pair. Such redundancies unnecessarily consumecircuit area and power. A need therefore exists for multi-dimensionalFIR filters that reduce the number of redundancies.

SUMMARY OF THE INVENTION

Generally, multi-dimensional finite impulse response filters in hybridand transpose forms are disclosed. The present invention recognizes thatmulti-dimensional signals can be expressed in a vector (or matrix) formto allow multi-dimensional signals to be processed collectively, ratherthan as a series of independent computations. The present inventionextends known hybrid and transpose FIR filters to the multi-dimensionalcase to allow multi-dimensional signals to be processed with reducedredundancies. In contrast to the above described scalar FIRimplementations, the input signals that are applied to the disclosedmulti-dimensional FIR filters are vectors with multidimensionalcomponents. In addition, the disclosed FIR filters include multipliersthat perform matrix multiplications with multiple coefficients, andadders for performing vector additions with multiple inputs and outputs.

The z-transforms are provided for the disclosed hybrid and transposemulti-dimensional FIR filters. The multi-dimensional finite impulseresponse filters used herein have matrix coefficients. Each FIR filtercomprises N multipliers having taps with filter weights or tapcoefficients, W_(N), respectively. These filter weights, W_(N),represent matrix multiplicands to be multiplied by input data traversingan input path. The multipliers each perform a matrix multiplicationoperation The output of each FIR filter can be expressed as:Y(z)=H(z)Tx(z),where H(z) is a matrix, defined herein for both the transpose and hybridforms, and Tx(z) is the vector representation of the multi-dimensionalsignal. Each adder performs a vector addition of the multiplecomponents. The disclosed multi-dimensional FIR filters may be employedfor example, to cancel noise in a twisted pair environment, such as echoand near and far end cross-talk, or to equalize a received signal.

A more complete understanding of the present invention, as well asfurther features and advantages of the present invention, will beobtained by reference to the following detailed description anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a conventional finite impulse response filter inhybrid form having three modules;

FIG. 2 illustrates a finite impulse response filter in hybrid formincorporating features of the present invention; and

FIG. 3 illustrates a finite impulse response filter in transpose formincorporating features of the present invention.

DETAILED DESCRIPTION

As previously indicated, it has been found that conventional near endcross-talk and echo cancellers typically consider the same signal on agiven twisted pair multiple times in order to reduce the echo on thesame twisted pair, as well as the cross-talk on each of the othertwisted pairs. For example, a transmitted signal Tx1 is used by an echocanceller to remove echo from the received signal on the first twistedpair, and is also used by the near end cancellers for twisted pails 2through 4. Thus, redundancies result from the same operation (e.g, adelay) being applied to the same input (e g., Tx1) four times. Thepresent invention recognizes that the redundancies can be reduced oreven removed entirely by processing multi-dimensional signals, such asthe various components of a received signal, in a vector form, on amulti-dimensional FIR filter. Thus, the various components of themulti-dimensional signal are processed collectively, rather than as aseries of independent computations. It is noted that a vector is merelya special case of a matrix (where the matrix has only a single column),and in some applications, the multi-dimensional signal may be betterexpressed as a matrix and in other applications, the multi-dimensionalsignal may be better expressed as a vector, as would be apparent to aperson of ordinary skill in the art.

FIG. 2 illustrates a multi-dimensional FIR filter 200 in hybrid formincorporating features of the present invention. Thus, the presentinvention extends the hybrid form of FIR filters to multi-dimensionalfilters. As shown in FIG. 2, the scalar representation of the inputsignals are replaced by vectors with multidimensional components, thescalar multiplications become matrix multiplications with multiplecoefficients, and the scalar additions become vector additions withmultiple inputs and outputs (relative to the conventional hybrid FIRfilter 100 shown in FIG. 1).

The FIR filter 200 shown in FIG. 2 has three modules 210-1 through210-3. Each module, such as module 210-1, provides three taps atmultipliers 215-1, 215-2 and 215-3, respectively. Each module 210includes the same number of delay elements as the number of taps.Specifically, delay elements 205-1 and 205-2 are disposed on input path201, and delay element 205-3 is disposed on output path 211. Delayelement 205-2 is inserted between multipliers 215-1 and 215-2. Delayelement 205-2 is inserted between multipliers 215-2 and 215-3. Adder220-3 receives a delayed sum generated by adder 220-4 and a productgenerated by multiplier 215-3 and generates a sum. Adder 220-2 receivesthe sum generated by adder 220-3 and a product generated by multiplier215-2 and generates a sum. Adder 220-1, disposed on output path 211,receives the sum generated by adder 220-2 and a product generated bymultiplier 215-1 and generates a sum.

According to one aspect of the invention, the filter weights for themodules 210-1 through 210-3 shown in FIG. 2 are matrix values, W₀through W₈. With the above filter arrangement, the z-transform of thetransfer function of filter 100, H(z), can be expressed as follows:H(z)=z ⁻¹ {W ₀ +W ₁ z ⁻¹ +W ₂ z ⁻² }+z ⁻³ {W ₃ +W ₄ z ⁻¹ +W ₅ z⁻²}+  (1)where the first term z⁻¹{W₀+W₁z⁻¹+W₂z⁻²} corresponds to module 210-1;and the second term z⁻³{W₃+W₄z⁻¹+W₅z⁻²} corresponds to module 210-2.

Generally, the multi-dimensional finite impulse response (FIR) filtersof the present invention process multi-dimensional signals in a vector(or matrix) form. In this manner, the multi-dimensional signal can beprocessed collectively, rather than as a series of independentcomputations. The present invention recognizes that multi-dimensionalsignals, such as the received signal for each twisted pair in a crosstalk canceller, can be expressed in a vector form. The vectorrepresentation of a received signal includes, for example, fourelements, Rx1, Rx2, Rx3 and Rx4, in the four twisted pair case.

The multi-dimensional finite impulse response filters used herein havematrix coefficients. As shown in FIG. 2, the FIR filter 200 comprises Nmultipliers 215 having taps with filter weights or tap coefficients,W_(N), respectively. These filter weights represent matrix multiplicandsto be multiplied by input data traversing input path 201. It is notedthat for a conventional implementation, the weights, w_(n), applied toeach filter tap are scalar values while the weights, W_(n), applied toeach filter tap in the present invention are matrix values (such as a 4by 4 matrix).

The multipliers 215 each perform a matrix multiplication operation. Forexample, for four twisted pairs in a cross talk canceller, eachmultiplication is a multiplication of a 4 by 4 matrix by a foulcomponent vector. As shown in FIG. 2, the output of the FIR filter 200can be expressed as:Y(z)=H(z)Tx(z),where H(z) is a matrix, defined above, and Tx(z) is the vectorrepresentation of the multi-dimensional signal. In addition, the adders220-1 through 220-9 each perform a vector addition of the multiplecomponents. The hybrid form FIR filter 200, shown in FIG. 2, may beemployed for example, to cancel noise in a twisted pair environment,such as echo and near and far end cross-talk, or to equalize a receivedsignal, as described in U.S. patent application Ser. No. 10/610,334,entitled, “Method And Apparatus For Reducing Cross-Talk With ReducedRedundancies,” incorporated by reference herein.

FIG. 3 illustrates a multi-dimensional FIR filter in transpose form,incorporating features of the present invention. Thus, the presentinvention extends the transpose form of FIR filters to multi-dimensionalfilters. As shown in FIG. 3, the scalar representation of the inputsignals are replaced by vectors with multidimensional components, thescalar multiplications become matrix multiplications with multiplecoefficients, and the scalar additions become vector additions withmultiple inputs and outputs, relative to a conventional transpose formFIR filter.

The z-transform of the transfer function of the FIR filter 300, H(z),is:H(z)=W ₀ +W ₁ z ⁻¹ +W ₂ z ⁻² +W ₃ z ⁻³  (2)For example, the first weight term, W₀, in the above equationcorresponds to no delay and the second term, W₁z⁻¹, corresponds to onestage of delay. It is noted that for a conventional implementation, theweights, w_(n), applied to each filter tap are scalar values while theweights, W_(n), applied to each filter tap in the filter 300 of thepresent invention are matrix values (such as a 4 by 4 matrix). For afurther discussion of conventional transpose form finite impulseresponse filters, see, for example, U.S. Pat. No. 5,983,254,incorporated by reference herein. It is noted that unlike the directform of FIR filter, there are no delay elements in the input path of thetranspose form.

Rather, in accordance with the transpose form, each of the delayelements are disposed on output path 311 and are each inserted betweenmultiplier/adder pairs 315, 320. Thus, the critical path in themulti-dimensional filter 300 includes a multiplier 315 and an adder 320,resulting in the maximum computation delay incurred by a multiplicationand an addition. Furthermore, such computation delay does not depend onthe length, or the number of taps, of filter 300.

As indicated above, the multi-dimensional finite impulse responsefilters used herein have matrix coefficients. The FIR filter 300 of FIG.3 comprises N multipliers 315 having taps with filter weights or tapcoefficients, W_(N), respectively. These filter weights represent matrixmultiplicands to be multiplied by input data traversing input path 301.It is noted that for a conventional implementation, the weights, w_(n),applied to each filter tap awe scalar values while the weights, W_(n),applied to each filter tap in the present invention are matrix values(such as a 4 by 4 matrix).

The multipliers 315 each perform a matrix multiplication operation. Forexample, for four twisted pairs in a cross talk canceller, eachmultiplication is a multiplication of a 4 by 4 matrix by a fourcomponent vector. As shown in FIG. 3, the output of the FIR filter 300can be expressed as:Y(z)=H(z)Tx(z),where H(z) is a matrix, defined above, and Tx(z) is the vectorrepresentation of the multi-dimensional signal. In addition, the adders320-1 through 320-9 each perform a vector addition of the multiplecomponents. The transpose form FIR filter 300, shown in FIG. 3, may beemployed for example, to cancel noise in a twisted pair environment,such as echo and near and far end cross-talk, or to equalize a receivedsignal, as described in U.S. patent application Ser. No. 10/610,334,entitled, “Method And Apparatus For Reducing Cross-Talk With ReducedRedundancies,” incorporated by reference herein.

It is to be understood that the embodiments and variations shown anddescribed herein are merely illustrative of the principles of thisinvention and that various modifications may be implemented by thoseskilled in the art without departing from the scope and spirit of theinvention.

I claim:
 1. A method for processing a multi-dimensional signal to removefar-end cross-talk, said method comprising the steps of: aggregating aplurality of single dimension signals to form said multi-dimensionalsignal; representing said multi-dimensional signal as a vector, whereinsaid vector includes a component for each of said dimensions; andapplying said vector to a hybrid multi-dimensional digital filterapparatus to remove said far-end cross-talk, wherein said hybridmulti-dimensional digital filter apparatus has matrix coefficients suchthat said vector is multiplied by said matrix coefficients, wherein saidhybrid multi-dimensional digital filter apparatus comprises a pluralityof delay elements; a plurality of adders performing at least one vectoraddition; a first path for transporting input data to each of themultipliers of the filter, and a second path for transporting data fromthe plurality of adders to an output thereof, wherein at least one ofsaid plurality of delay elements being disposed on said second path, therest of said plurality of delay elements being disposed on said firstpath.
 2. The method of claim 1, wherein said applying step removes echofrom a received signal.
 3. The method of claim 1, wherein said applyingstep removes noise from a received signal.
 4. The method of claim 1,wherein said applying step equalizes a received signal.
 5. An apparatusfor processing a multi-dimensional signal to remove far-end cross-talk,comprising: means for aggregating a plurality of single dimensionsignals to form said multi-dimensional signal; an input port forreceiving said multi-dimensional signal as a vector, wherein said vectorincludes a component for each of said dimensions; and a hybridmulti-dimensional digital filter having matrix coefficients forprocessing said vector by multiplying said vector by said matrixcoefficients to remove said far-end cross-talk, wherein said hybridmulti-dimensional digital filter apparatus comprises a plurality ofdelay elements; a plurality of adders each performing at least onevector addition; a first path for transporting input data to each of themultipliers of the filter, and a second path for transporting data fromthe plurality of adders to an output thereof, wherein at least one ofsaid plurality of delay elements being disposed on said second path, therest of said plurality of delay elements being disposed on said firstpath.
 6. The apparatus of claim 5, wherein said multi-dimensional filterremoves noise from a received signal.